Atkin-Lehner |
2+ 3+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12696a |
Isogeny class |
Conductor |
12696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
236544 |
Modular degree for the optimal curve |
Δ |
-4169004688233508608 = -1 · 28 · 314 · 237 |
Discriminant |
Eigenvalues |
2+ 3+ 0 2 0 2 -8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1538508,-740537676] |
[a1,a2,a3,a4,a6] |
j |
-10627137250000/110008287 |
j-invariant |
L |
1.2192678197734 |
L(r)(E,1)/r! |
Ω |
0.06773710109852 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25392f1 101568p1 38088q1 552b1 |
Quadratic twists by: -4 8 -3 -23 |